Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Novosibirsk participants

Research of wave modes on a film of a viscous ferromagnetic fluid flowing on the vertical cylinder

Samatov S.N., Tsvelodub O.Y.

Institute of Thermophysics,
SB RAS (Novosibirsk)

Within Noyringer – Rosensweig model the approximated equation showing behaviour of disturbances on a surface of a thin film of a viscous ferromagnetic fluid flowing by gravity along a cylindrical conductor is deduced. On one the alternating current is flows . The following assumptions will be used: the rate of flow is small - Reynolds number about unit, the coefficient of surface tension large - Weber number is much greater units, radius of the cylinder is much greater of the reference longitudinal size of disturbances, the frequency of alternating-current was guessed small - noninductive approximation. In this case consideration of a problem is reduced to the analysis of the solutions of one non-linear equation for deviation of film thickness from a unperturbed level. For disturbances with small, but final amplitudes in this evolution equation it is possible to limit by quadratic nonlinearity.

In this work some typical solutions of the obtained equation are numerically constructed. As a result, it is demonstrated, as there is a birth of waves from the trivial solution in a neighbourhood of neutral wave numbers.

This work is supported by RFFI (grant N 00-01-00849 ) and INTAS (grant N 99-1107.

Note. Abstracts are published in author's edition

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